trading intensity

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Trade intensity and purchasing power parity

Dooyeon Cho a,1, Antonio Doblas-Madrid b,a Department of Economics, Kookmin University, Seoul 136-702, Republic of Koreab Department of Economics, Michigan State University, 110 Marshall-Adams Hall, East Lansing, MI 48824, USA

a b s t r a c ta r t i c l e i n f o

Article history:

Received 19 April 2011

Received in revised form 17 December 2013

Accepted 15 January 2014Available online xxxx

JEL classication:

C13

C52

F31

F47

Keywords:

Trade intensity

Deviations from PPP

Exchange rate volatility

Carry trades

Mean reversion

In this paper, we seek to contributeto thePPP literatureby presenting evidence of a link between trade intensity

and exchange rate dynamics. We rst establish a negative effect of trade intensity on exchange rate volatility

using panel regressions, with distance as an instrument to correct for endogeneity. We also estimate a nonlinear

model of mean reversion to compute half-lives of deviations of bilateral exchange rates from the levels dictated

by relative PPP, and nd these half-lives to be signicantly shorter for high trade intensity currency pairs. This

result does not appear to be driven by Central Bank intervention. Finally, we show that conditioning on PPP

may help improve the performance of popular currency trading strategies, such as the carry trade, especially

for low trade intensity currency pairs.

2014 Elsevier B.V. All rights reserved.

1. Introduction

For international economists, exchange rate determination is a topic

of perennial interest and a formidable challenge. While some models

such as Taylor et al. (2001), Molodtsova and Papell (2009), Mark

(1995)and othershave outperformedMeese and Rogoff's (1983)

famous random walk, the fraction of movement explained, let alone

predicted, remains small.

According toRogoff (2008), the most consistent empirical regularity

is purchasing power parity (PPP). Despite their volatility, real exchange

rates appear to revert back to long-run averages as predicted by relative

PPP. In this paper, we investigate whether the degree of trade intensity

(TI henceforth) betweentwo countries affectsmeanreversion in their bi-

lateral realexchange rate. Our hypothesis is straightforward.PPP is based

on the Law of One Price,which in turn relies on goods arbitrage. As devi-

ations from PPP widen, the number of goods for which price differences

exceed transaction costs should increase. As agents exploit emerging op-

portunities forgoods arbitrage, they increase demand for goods in cheap

locations and supply in expensive ones. This reequilibration should be

strongerbetween close trading partners, presumably due to lower trans-

action costswhich include transport and tariffs, but also xed costs like

translating,advertising,licensing, etc.Sooner or later, goods trade should

translate into currency trades and affect nominal exchange rates, which

typically drive most of the variability in real exchange rates. Although

turnover in foreign exchange (forex) markets far exceeds export values,

this stabilizing effect of exports on exchange rates need not be insigni-

cant. In fact, forex market participants often claim that exports matter

because, while speculative traders drive most volume, they open and

close positions very frequently. By contrast, export driven transactions

generate positions that are opened but never closed, exerting pressure

on exchange rates in a much more consistent direction. Moreover, if

investors take trade into accountfor example by favoring countries

with trade surpluseswhen deciding which currencies to buy, specula-

tive trades may actually complement the effect of exports.

We consider a sample of 91 currency pairs involving 14 countries

over the period 19802005. To dene and quantify TI, we largely follow

Betts and Kehoe (2008). Our measures of TI between countries A and B

arebasedon themagnitudeof thebilateral trade between them, relative

to A's (and/or B's) total trade. Not surprisingly, TI and exchange rate

volatility are negatively correlated in our sample. This correlation is

likely a product of causality in both directions. As mentioned above, TI

may reduce volatility through goods arbitrage, which exerts pressure

to reduce deviations from PPP. In the other direction, there is the

argumentoften brought up in defense ofxed exchange ratesthat

lower exchange rate volatility may increase trade between countries

by reducing uncertainty and hedging costs. Since we are primarilyinter-

ested in the rst direction of causality, we begin the analysis by

implementing panel regressions with exchange rate volatility as a

Journal of International Economics xxx (2014) xxxxxx

Corresponding author. Tel.: +1 517 355 8320; fax: +1 517 432 1068.

E-mailaddresses: [email protected] (D.Cho),[email protected] (A.Doblas-Madrid).1 Tel.: +82 2 910 5617; fax: +82 2 910 4519.

INEC-02750; No of Pages 16

0022-1996/$ see front matter 2014 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.jinteco.2014.01.007

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Please cite this article as: Cho, D., Doblas-Madrid, A., Trade intensity and purchasing power parity, J. Int. Econ. (2014), http://dx.doi.org/10.1016/j.jinteco.2014.01.007
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dependent variable and TI as one of our independent variables, using

the distance between two countries as an instrument. This approach is

similar to that ofBroda and Romalis (2009). Coefcient estimates

from these regressions across various specications show a negative

effect of TI between two countries on their bilateral real exchange

rate. We also nd that, consistent with the literature on carry trades

(see, for instance,Bhansali (2007)) exchange rate volatility increases

with the absolute value of interest rate differentials. While most of the

currencies in our sample are

oating during all or most of the sampleperiod,there are some exceptions. However, our results remain qualita-

tively unchanged when we drop or control for pegged currency pairs.

Our results are moreover robust to the use of different measures of

exchange rate volatility and TI, and to considering only major currency

pairs, as opposed to minor/exotic pairs. Finally, the results are qualita-

tively preserved when we restrict attention to just the rst, or second

half, of the 19802005 period.

Motivated byMichael et al. (1997)and Taylor et al. (2001), who

provide evidence of nonlinear mean reversion in a number of major real

exchange rates, we quantify the size and persistence of PPP deviations

using a nonlinear model. Specically, we estimate an exponential smooth

transition autoregressive (ESTAR) model, which allows the speed at

which exchange rates converge to their long-run equilibrium values to

depend on the size of the deviations. The model allows for the possibility

that real exchange rates may behave like unit root processes when close

to their long-run equilibrium levels, while becoming increasingly mean-

reverting as they move away from equilibrium. For our comparison, we

restrict attention to 35 highest and 35 lowest currency pairs, as ordered

by TI. We make this choice to ensure that the difference in trade intensi-

ties between the two sets of currency pairs is so large and stable that var-

iations of TI over time are negligible in comparison to the differences in

trade intensities between the two sets of pairs. After estimating the

ESTAR models, we investigate the dynamic adjustment in response to

shocks to real exchange rates in the estimated ESTAR model by comput-

ing the generalized impulse response functions (GIs) using the Monte

Carlo integration method introduced byGallant et al. (1993). We nd

that, as hypothesized, the estimates of the half-lives of deviations from

PPPfor a given currency pair are higher the less intense the traderelation-

ship between two countries. For currency pairs in the high TI group, theaveragehalf-life of deviationsfromPPP is given by 20.20 months, where-

as for lowTI pairs, it is 26.34 months. Moreover, this nding is statistically

signicant.

Wealso verify that ourresult is not driven by CentralBankinterven-

tion. That is, a possible concern when interpreting our results is that, if

Central Banks exhibit more fear ofoatingin response to exchange

rate uctuations against important trading partners, the observed

differences in volatility may primarily be due to ofcial reserve transac-

tions, rather than trade. To address this concern, we consider various

proxies for interventionspecically the volatility of reserves and inter-

est rates, following Calvo and Reinhart (2002). To judge by these

measures, government intervention is unlikely to be the reason for

faster convergence in high TI cases, since the degree of currency inter-

vention is typically lower for high TI currency pairs.Finally, we investigate whether ourndings on TI and mean reversion

can be used to improve the performance of forex trading strategies, such

as the carry trade. To do this, we perform an exercise similar toJord and

Taylor (2012). We simulate a PPP-augmented carry trade, which gives a

buy signal only if there is a positive interest rate differential and the

high interest currency is undervalued according to relative PPP. The crite-

rion to decide whether a currency is over- or undervalued is simply

whether the (lagged) real exchange rate is above or below its historical

average by a percentage . (The higher , the greater of degree of under-

valuation needed to satisfy the PPP condition.) We compare the perfor-

mance of this PPP-augmented carry trade to a plain carry trade, which

chases high interest rate differentials regardless of PPP valuations. We

do this separately for a high TI and for a low TI portfolio. Across all our

specicationsof thecarry trade, thePPP-augmentedstrategy outperforms

the plain carry, in the sense that it has higher Sharpe ratios. These gains

from conditioning on PPP tend to be greater in thelow TI portfolio. More-

over, theoptimal is also higher in thelow TI case. While theseresultsare

obtained in sample, we nd that the same patterns do hold out-of-

sample, although the gains from conditioning on PPP become smaller,

especially in the high TI group.

The rest of thepaperis organized as follows.In Section 2, we describe

our data and dene variables. In Section 3, we provide evidence of a link-

age between TI and exchange rate volatility using panel regressions. InSection 4, we present and discuss empirical results from ESTAR models.

We also conduct and discuss stationary tests for estimated ESTAR

models. Further, we investigate whetherour half-life estimates aremain-

ly driven by government intervention. In Section 5, weapplyourndings

to currency trading strategies. InSection 6, we conclude.

2. Data and variable denitions

2.1. Data sources

We collect monthly nominal exchange rates vis--vis the US Dollar

(USD) from January 1980 through December 2008 for the following

13 currencies: Australian Dollar (AUD), Canadian Dollar (CAD),

Euro/Deutsche Mark (EUR/DEM), Great Britain Pound (GBP), Japanese

Yen (JPY), Korean Won (KRW), Mexican Peso (MXN), New Zealand

Dollar (NZD), Norwegian Krone (NOK), Singapore Dollar (SGD),

Swedish Krona (SEK), Swiss Franc (CHF), and Turkish Lira (TRY). To

choose the currencies, we follow the BIS Triennial Central Bank Survey,

and focus on the 20 most traded currencies in 2010. Six of the top

twenty currencies, the Hong Kong Dollar (in 8th place), Indian Rupee,

Russian Ruble, Chinese Renminbi, Polish Zloty (in places 1518), and

the South African Rand (in place number 20) were dropped due to

data limitations, being xed for most of the sample period, or both.

Combining each of the 14 currencies with the rest, we obtain a total of

91 bilateral trade relationships and real exchange rates.

For all 14 currencies, we collect monthly money market interest

rates, price indices, in particular the consumer price index (CPI), and

foreign exchange reserves. We retrieve these data from the IMF's

International Financial Statistics(IFS) database. Data for annual exportsused to measure trade intensity (TI) are borrowed from Betts and

Kehoe (2008).2

2.2. Measuring exchange rate volatility and trade intensity

The aim of this paper is to investigate the link between TI and ex-

change rate volatility. Our hypothesis is that the more intense the

trade relationshipbetween two countries, the less volatile their bilateral

real exchange rate. To investigate the link between them, we start by

dening our measures of exchange rate volatility and TI.

The real exchange rateQtis dened as

Qt StPtPt

; 1

where Stis the nominal exchange rate measured as the price of oneunit

of domestic currency in terms of foreign currency, and Ptand Pt denote

domestic and foreign price levels, respectively. The log real exchange

rateqtis given by

qt stptpt; 2

2 The data along with a dataAppendix Afor annual exports to measure TI are publicly

available at Timothy Kehoe's webpage, http://www.econ.umn.edu/~tkehoe/research.

html.

2 D. Cho, A. Doblas-Madrid / Journal of International Economics xxx (2014) xxxxxx

http://www.econ.umn.edu/~tkehoe/research.html)http://www.econ.umn.edu/~tkehoe/research.html)http://www.econ.umn.edu/~tkehoe/research.html)http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://www.econ.umn.edu/~tkehoe/research.html)http://www.econ.umn.edu/~tkehoe/research.html)


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wherest,ptandptdenote the logarithms of their respective uppercase

variables. The real exchange rate is the price of one unit of domestic

goods in terms of foreign goods.

To measure exchange rate volatilityvolijbetween countriesi andj,

we calculate the standard deviation of the monthly logarithms of the

bilateral real exchange rates over the one-year period for each currency

pair. (As a robustness check, we will also use different time windows

such as the three-year window and six-year window.) Specically,

volijis given by

volij 1

T1

XTt1

qij;tqij

2" #12; 3

whereqij,tis the monthly logarithm of the bilateral real exchange rate

between countriesiandj, andqijis the mean value ofqij,tover a period

ofTmonths.

We dene two alternative measures of TI, which aim to capture the

relative importance of a bilateral trade relationship as a fraction of each

country's total trade. FollowingBetts and Kehoe (2008), we dene the

maximum TI variabletradeintX,Y,tmax between countriesXandYas follows

tradeintmaxX;Y;t

max

exportX;Y;texportY;X;tXall

exportX;i;tXall

exporti;X;t;


exportY;i;tXall

exporti;Y;t

8>>>:

9>>=>>;;4

whereexportX,Y,tis measured as free on board (f.o.b.) merchandise ex-

portsfromcountryXto country Yat year t, measured in year tUS dollars.

According to this denition, TI only needs to be high for one of the

two countries in the bilateral trade relationship. To see how to apply

this denition, consider for example the KoreaUS relationship.

With Korea accounting for just 5.3% of US trade, and the United

States accounting for 39.6% of Korean trade, tradeintX,Y,tmax equals 39.6.

We also denetradeintX,Y,tavg as an alternative measure to Eq.(4). Instead

of picking the highest and discarding the lowest percentage, this

measure takes both percentages into account. More precisely,

average TItradeintX,Y,tavg between countriesXandYis dened as

tradeintavgX;Y;tavg


exportX;i;tX

all

exporti;X;t;


exportY;i;tX

all

exporti;Y;t

8>>>:

9>>=>>;:5

Thus, this measure averages the two fractions in the bilateral trade

relationship. If we apply the denition in Eq. (5) to the KoreaUS

example given above, we obtain 22.5% instead of 39.6% between Korea

and the United States. Both TI measuresaveraged over the period

19802005are reported inTable 1, panels (A) and (B) for all bilateral

trade relationships. FortradeintX,Y,tmax andtradeintX,Y,t

avg most observations

are between 0 and 0.4, and between 0 and 0.2, respectively, with a

few outliers above these levels. In the analyses that follow, we will

therefore always verify that our results are not driven by these outliers.

InFig. 1(A) and (B), we show scatter plots of exchange rate volatility

against TI (maximum) and TI (average), respectively, for the 91 curren-

cy pairs listed inTable 1. In addition to the presence of outliers, the

scatter plots show a negative correlation between volatility and both

TI measures.

3. Panel regressions with distance as an instrument

The scatter plots fromFig. 1show a negative correlation between TI

and volatility, with the associated OLS regressions producing a negative

slope that is signicant at the 1% level for both TI measures.3 These

regressions, however, are fraught with obvious endogeneity problems,

since causality between volatility and TI runs both ways. To address

this issue, in our preliminary regressions we employ an instrumental

variable (IV) estimation approach. Specically, we use the distance

between two countries as an instrument for TI. Clearly, distance

between two countries is exogenous and not determined by exchange

rate volatility. Moreover, distance is also an appropriate proxy variable

for TI sinceas predicted by gravity modelscountries that are closer

to each other tend to trade more. We thus estimate the following IVpanel regression equation,

volij;tvolij;t1 tradeintij;t absidij;tXN1i1

divij;t 6

where is an intercept term,volij,tis exchange rate volatility, tradeintij,tis TI (maximum) or TI (average), absidij,tis the absolute value of the

interest rate differential between two countries,i andj,diis a dummy

variable for each countryi (Ndenotes the total number of countries),

andvij,tis an error term.Table 2presents results from IV estimation

using panel data for the effects of TI on real exchange rate volatility.

Our estimates are negative and statistically signicant at the 1% level

for both measures of TI, maximum and average. Besides this mainnding, we also nd that exchange rate volatility increases with the

absolute value of interest rate differentials, which is consistent with

the view that carry tradeswhich are often seen as drivers of currency

trends and sharp reversalslead to an increase in volatility of the

exchange rates between investment and funding currencies.4

InTables 3A, 3B, 3C, 3D, and 3E, we conduct a number of robust-

ness checks for results from IV estimation using panel data: (a) we

drop/control for xed exchange rates, (b) we exclude outliers for the

real exchange ratevolatilityvariable andtheTI variable, (c)we subsample

by subperiods: 19801992 and 19932005, (d) we subsample by major

vs. minor, or exotic, currency pairs, and (e) we construct the volatility

variable using different time windows, in particular 3 and 6 years.

Regarding the rst robustness test (a), it is important to verify that,

since exchange rate stability is believed to promote trade, our resultsare not primarily driven by the choice of exchange rate regime. In this

section, we follow IMF ofcial classications of regimes, as compiled

byReinhart and Rogoff (2009). (InSection 4, we will revisit the issue,

focusing on de facto intervention rather than ofcially reported ex-

change rate regimes.) Most currencies in our sample are classied as

oating for most of the sample period, but there are a few exceptions.

Most importantly, in some years, a few countries pegged their curren-

cies to trade-weighted indices, creating a negative link between trade

and volatility, almost by construction. This includes Norway and

Sweden over 198092 and Singapore over 19802005. We could not

nd a reasonable wayto control forthis, since addinga proxy measuring

the degree ofxingproportionally to TI is akin to having TI twice. We

have thus excluded all pairs involving NOK, SEK, and SGD over the rele-

vant years. In a few other casesnamely USD/KRW over 198096, USD/

MXN over 19801993, USD/TRY over 19801999, and CHF/EUR over

198081we encounter bilateral pegs. FollowingReinhart and Rogoff

(2009)we include as xed all varieties of constant and crawling pegs

with bands no wider than 2%.5 We control for these cases using a

xeddummy variable. We report results from this robustness test in

Table 3A. While these changes somewhat reduce the absolute value of

the negative coefcient between TI and volatility, the coefcient re-

mains signicant at the 1% level, and thus, our qualitative results

3 When we drop theUSD/CAD orUSD/MXNpairor both, thesignicance remainsat 1%

for average TI, but becomes 5% for the maximum TI measure.

4 When we drop the interest rate differential, the negative relation between TI and ex-

change rate volatility remains unchanged.5 Note that this denition excludes the well-known episode corresponding to Britain's

ERM membership over 198992. While the Pound was pegged to the German Mark, the

width of the band was 6%, and thus the regime is classi

ed as

oating.

3D. Cho, A. Doblas-Madrid / Journal of International Economics xxx (2014) xxxxxx

http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007http://dx.doi.org/10.1016/j.jinteco.2014.01.007


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continue to hold. Moreover, as expected, the coefcient associated with

thexeddummy is negative and signicant at the 1% level.6

Next, in Table 3B we truncate outliers of the dependent variable, real

exchange rate volatility, by excluding all observations that are more

than two standard deviations from the mean in any period t. This has

little impact on the results. Next, we also truncate outliers of the TI var-

iable by excluding all observations that are included in the highest 2%(this leads to dropping 52 observations for both TI (maximum) and TI

(average), respectively.). Truncating outliers of the TI variable also

leaves our results unaltered, as can be seen inTable 3B. Second, we

divide the entire sample period into two subperiods: 19801992

(rst half) and 19932005 (second half). As reported inTable 3C, the

slope coefcients for TI on volatility are greater in absolute value, i.e.,

more negative, in the rst half of the sample period. Qualitatively,

however, results are similar across both subperiods, with coefcients

remaining negative and signicant at the 1% level. Third, we investigate

whether our results are different for major currency crosses, which add

up to 42 outof our total of 91, and minor/exotic currency crosses, which

include the remaining 49 out of 91.7 This robustness test is driven by

potential concerns about volatility differences being driven by market

liquidity, which is greater for major currency pairs. As can be seenfromTable 3D, the results in both subsamples are almost exactly equal

to each other and to the overall results reported inTable 2. Finally, we

verify that our results are not sensitive to changing the width of the

time window in the denition of our volatility variable, set at 1 year in

the baseline regressions. Results with 3 and 6 year windows are report-

ed inTable 3E.Clearly, the use of different time windows has virtually

no effect on the estimated coefcients for the other variables of interest.

Overall, the negative relationship between TI and exchange rate

volatility holds up well across the different robustness tests.

4. Estimation results from ESTAR models

While the previous section presents evidence that TI reduces ex-

change rate volatility, a related question is whether TI is also associated

with faster convergence of exchange rates to the values predicted by

relative PPP. To do this, we compare whether the half lives of PPP devi-

ations differ between the set of 35 pairs with the highest TI and the set

of 35 pairs with the lowest TI.8 Given the evidence of nonlinearity in

mean reversion presented byTaylor et al. (2001), we compute half-

lives of PPP deviations using an exponential smooth transition

autoregressive (ESTAR) model.

While we provide details in theAppendix A, in broad strokes the

ESTAR model can be described as follows. There is a lower regime in

which PPP deviations are small. In this regime, persistence is mainlygoverned by a parameter , which can be negative if there is mean

reversion, but can also be zero or positive, since unit root or explosive

dynamics arepossible.As PPP deviations grow, however, there is a grad-

ualshift to an upper regime in which persistence is governed by +*.

By assumption, the upper regime is mean reverting, and thus, it must be

that* b0 and +* b 0. A transition function, parameterized by slope

parameter, determines the speed of transition from the lower to the

upper regime as PPP deviations grow. Standardized deviations are

given by qtdc 2=qtd, where qt d is the d-period lagged realexchange rate, qtd is the standard deviation and the location parame-

ter cis the estimated mean level that the exchange rate should revert to.

Table 1

Trade intensity matrices.

Australia Canada Germany Great Britain Japan Korea Mexico New Zealand Norway Singapore Sweden Switzerland Turkey United States

(A) Trade intensity (maximum) matrix

Australia

Canada 0.02601

Germany 0.06396 0.02146

Great Britain 0.08558 0.03660 0.31786

Japan 0.32536 0.05063 0.10273 0.08117

Kor ea 0.0 7259 0.031 15 0.0 6426 0 .03 86 1 0 .33 182Mexico 0.00293 0.01976 0.03143 0.01383 0.04977 0.01008

New Zealand 0.32575 0.02335 0.04520 0.10231 0.20590 0.03699 0.00768

Norway 0.00392 0.03894 0.22720 0.31445 0.04263 0.01477 0.00137 0.00166

Singapore 0.06799 0.01110 0.07427 0.06522 0.29280 0.07174 0.00489 0.03538 0.00882

Sweden 0.01488 0.01783 0.31505 0.20161 0.05280 0.01292 0.00626 0.00837 0.23248 0.00897

Switzerland 0.01346 0.01603 0.51414 0.12076 0.06734 0.01385 0.00794 0.00764 0.01491 0.01473 0.03654

Turkey 0.00901 0.01461 0.43699 0.13872 0.05691 0.02526 0.00169 0.00222 0.00783 0.00867 0.02602 0.05658

United States 0.23868 0.86214 0.24199 0.28871 0.51744 0.39648 0.86181 0.19756 0.09605 0.37439 0.15974 0.17966 0.21514

(B) Trade intensity (average) matrix

Australia

Canada 0.01590

Germany 0.03996 0.02015

Great Britain 0.05618 0.03124 0.28456

Japan 0.19591 0.04817 0.09314 0.06673

Kor ea 0.0 5802 0.020 94 0.0 4521 0 .02 91 0 0 .22 051

Mexico 0.00221 0.01374 0.02268 0.01025 0.03267 0.00922

New Zealand 0.20436 0.01234 0.02403 0.05530 0.10829 0.02128 0.00439Norway 0.00331 0.02219 0.13365 0.19205 0.02428 0.01088 0.00098 0.00114

Singapore 0.06602 0.00677 0.04702 0.04358 0.17784 0.06003 0.00367 0.02247 0.00741

Sweden 0.01479 0.01088 0.19629 0.13207 0.03167 0.01043 0.00494 0.00526 0.19729 0.00888

Switzerland 0.01226 0.01013 0.33322 0.08290 0.04181 0.01195 0.00672 0.00463 0.01181 0.01409 0.03347

Turkey 0.00603 0.00776 0.23547 0.07642 0.03020 0.01525 0.00099 0.00195 0.00585 0.00557 0.01757 0.03525

United States 0.12948 0.59842 0.16175 0.18303 0.36772 0.22461 0.49911 0.10091 0.05076 0.20369 0.08643 0.09857 0.11025

Note. Values for trade intensity (maximum) and trade intensity (average) averaged over the sample period 1980 2005 are reported.

6 In untabulated results, we also reran the regressions considering as xed and all pos-

sible combinations ofpairsamongKRW, MXN,and TRY, on thegrounds that, iftwo curren-

cies are pegged to theUSD,theyare pegged to each otheralthough in practice the bands

around the pegs signicantly weaken the degree to which pegging is transitive. In any

case, results were very similar to the baseline case.7 The most traded currency pairs in the foreign exchange market are called the major

currencypairs. Theyinvolve thecurrencies such as Australian Dollar(AUD),Canadian Dol-

lar (CAD), Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Franc (CHF),

and US Dollar (USD). On the other hand, the minor/exotic currency pairs are dened as

those pairs that are emerging economies rather than developed countries.

8 We use TI (average) to rank currency pairs. Using TI (maximum) instead of TI

(average) makes little difference.




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Further parameters1,,p 1 and1

,,p 1

capture higher-orderpersistence in the lower and upper regimes, respectively. Parameters

are estimated via nonlinear least squares (NLS).9

Having estimated the ESTAR model, we followKoop et al. (1996)to

generate generalized impulse response functions (GIs). (See the

Appendix Afor details.) The generated GIs are depicted inFig. 2(A)

and (B). In the graphs, GIs for high TI currency pairs appear to decay

faster. This impression is conrmed when we calculate half-lives of

PPP deviations, which are reported in Table 4for high and low TI

pairs. Typically, our estimates of the half-lives of deviations from PPP

for a given currency pair are higher the less intense the trade relation-

ship between two countries. More specically, the average half-life in

the high TI group is shorter than the average half-life in the low TI

group by about 6.1 months. Thet-statistic for the difference in means

test is 2.13, allowing us to reject the null hypothesis of no differencein means.10 Thus, the half-lives of deviations from PPP based on the

estimations of the ESTAR models and the generated GIs suggest that

deviations from PPP arecorrected fasterfor country pairs with relatively

more intense trade relationships.

It remains to be veried whether the nonstationarity of the ESTAR

model can be rejected. Although (+*) b 0 is obtained for all pairs,

verifying the statistical signicance of the nonstationarity result is a

bit involved. Tests to detect the presence of nonstationarity against

stationary STAR processes have been developed byKapetanios et al.

(2003, KSS henceforth) andBec et al. (2010, BBC henceforth). These

two tests compute Taylor series approximations to STAR models,which have been used in the linearity test proposed bySaikkonen and

Luukkonen (1988)and get the auxiliary regressions

ytXr2rr1

ryt1yrtd

Xpj1

jytj t;

wheret iid(0,2). Both tests are performed by the statistical signi-

cance of the parameters r1 ;; r2

. Norman (2009)summarizes

both testing procedures, and extends to allow for a delay parameter, d,

that is greater than one. He shows that the distributions of both

statistics ford N1 are the same as the case when d = 1. KSS setr1=

r2 = 2, and derive the limiting non-standard distribution of thet-statistic to test2= 0 against the null hypothesis of 2 b 0

tNL2

s:e:

2 :

BBCset r1 = 1, r2 = 2, andderivethe limiting non-standard distribu-

tion of the Wald statistic, FNL, to test 1=2= 0 against the null hy-

pothesis of1 0 or 2 0.11 Applying both tests to our currency

pairs with de-meaned data, we obtaint-values andF-values for the

KSS and BBC tests, respectively. Histograms of the obtained values are

plotted inFig. 3. Out of 35 high TI currency pairs, KSS tests reject the

null in 1 case at the 1% level, 8 cases at the 5% level, and 5 cases at the

10% level. Out of 35 low TI pairs, KSS tests reject the null in 6 cases atthe 1% level, 6 at the 5% level, and 1 at the 10% level. The corresponding

numbers for BBC tests are 3 cases at the 1% level, 5 at the 5% level, and

6 at the 10% level for high TI pairs, and 6 cases at the 1% level, 5 at the

5% level, and 3 at the 10% level forlow TI pairs. In terms of overall rejec-

tion rates for nonstationarity, these results are similar to those obtained

by KSS and BBC in their respective samples of real exchange rates. 12

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

Trade intensity (maximum)

VOL = 0.051- 0.031 TI_max (0.002) (0.008)

A)SCATTER PLOT OF REAL EXCHANGE RATEVOLATILITY AGAINST TRADE INTENSITY (MAXIMUM)

0 0.2 0.4 0.6 0.8 1

Trade intensity (average)

VOL = 0.051- 0.051 TI_avg

(0.002) (0.012)

B)SCATTER PLOT OF REAL EXCHANGE RATEVOLATILITY AGAINST TRADE INTENSITY (AVERAGE)

Realexchangeratevolatility

0

0.02

0.04

0.06

0.08

0.1

Realexchangerate

volatility

Fig. 1.Scatter plots of real exchange rate volatility against trade intensity for 91 currency

pairs involving 14 countries over the period 19802005. The straight line is depicted by

running the ordinary least squares (OLS) regression. OLS estimates are reported above,

and the corresponding standard errors are in parentheses.

Table 2

Effects of TI on real exchange rate volatility: IV estimation using panel data.

[1] [2] [3] [4]

Real exchange rate volatility

at timet 1

0.121*** 0.122***

(0.021) (0.021)

TI (maximum) 0.037*** 0.033***

(0.007) (0.008)

TI (average) 0.056*** 0.050***

(0.011) (0.012)

Interest rate differential inabsolute value

0 .034 *** 0.033*** 0.03 4*** 0 .034***(0.004) (0.004) (0.004) (0.004)

Intercept 0.045*** 0.045*** 0.039*** 0.039***

(0.003) (0.003) (0.003) (0.003)

No. of observations 2366 2366 2275 2275

Note. Results from IV estimation using panel data with country xed effects are reported.

The distance between two countries is used as an instrument to estimate the relationship

between trade intensity and real exchange rate volatility. The sample period is from

January 1980 to December 2005, and 91 currency pairs involving 14 countries are

included. The dependent variable is real exchange rate volatility. Standard errors are

reported in parentheses below the corresponding coefcients. Asterisks *, **, and ***

indicate 10%, 5%, and 1% statistical signicance, respectively.

9 The estimation results along with the estimated transition functions, plotted against

time for high and low TI currency pairs are available from the authors upon request.10 Althoughtrade is endogenous to the real exchangerate, the differences in TI between

these twosets of countrypairsvery large andstable. In spite of dramatic movementin real

exchangeratesthroughoutthe sampleperiod,TI forall low-intensity countrypairsremain

far below any high-intensity pair at all times.

11 KSSreport1%, 5%,and 10%asymptoticalcriticalvaluesin Table 1 on page364.Howev-

er,BBC do not provideany asymptotical criticalvalues, and Norman(2009) reports the5%

asymptoticalcritical value (10.13) using Monte Carlosimulations with 50,000replications

in his paper. We thank Stephen Norman for providing us with 1% and 10% asymptotical

critical values for the BBC testing procedure.12 KSS nd evidencethat the tNL test rejects thenullin 5 casesat the5% signicance level

andanother at the 10%signicancelevel outof 10 real exchange rates againstthe US Dol-

lar.BBC conclude thatthe FNL test rejects thenullin 11cases outof 28realexchange rates.




6/16

4.1. Half-lives and government intervention

We investigate whether theobserveddifferencesin volatilitymay be

due to Central Bank intervention in currency markets, orfear ofoating,

instead of trade. To inquire into this issue, we follow in the footsteps of

Calvo and Reinhart (2002), using volatility of reserves and interest rates

as proxies for intervention.13 We then examine whether there is an

association between half-lives of deviations from PPP and our measures

of government intervention.

We denote the absolute value of the percent change in foreign

exchange reserves by |F|/Fand the absolute value of the change in

interest rate by |it it 1|. Our rst intervention proxy is the frequencywith which |F|/Ffalls within a critical bound of 2.5%. The greater this

frequency, the less a country intervenes. This interpretation is straight-

forward, since purchases or sales of reserves are the most direct form of

intervention. For our second proxy, we interpret volatile interest rates

as evidence of attempts to stabilize the exchange rate. Thus, our second

variable is the percent of thetime that interest rates change by 400 basis

points (4%) or more vis--vis the previous month. The more often this

occurs, the greater the degree of intervention. InTable 5, we report

the observed frequencies over the period January 1980December

2008. By these two measures, Japan, Singapore and the United States

are examples of countries that tend to intervene least, whereas

Mexico and Turkey are among those that intervene most. To quantify

the overall degree of intervention, we simply rank the currencies, with

1 denoting the least intervened currency and 14 the most intervened.

Averaging a currency's two rank orders (one for reserves, one for inter-

est rates), we obtain a currency's overall intervention level. To evaluate

the amount of intervention for a currency pair, we again average the

overall intervention levels of the two currencies in the pair.

Comparing intervention rankings for high versus low TI currency

crosses, we obtain an average of 5.32 for high TI currency pairs, and 8.19

for low TI pairs.14 This suggests that our half-life estimates are not mainlydriven by government intervention. If anything, intervention may reduce

the observed differences, if it successfully mitigates uctuations in the

low TI group.

5. Application to currency trading

We investigate whether our results can help predict exchange rates

and formulate protable currency trading strategies. To do this, we

must keep in mind that the returns of a strategy depend not only on ex-

change rate movements, but also on interest rates. This is partly due to

Table 3BEffects of TI on real exchange rate volatility: Truncating outliers.

Robustness checks

Truncating outliers for real exchange rate volatility Truncating outliers for TI

[1] [2] [3] [4] [1] [2] [3] [4]

Real exchange rate volatility at timet 1 0.139*** 0.140*** 0.127*** 0.124***

(0.016) (0.016) (0.021) (0.021)

TI (maximum) 0.045*** 0.040*** 0.040*** 0.036***

(0.006) (0.006) (0.011) (0.011)

TI (average) 0.068*** 0.061*** 0.055*** 0.049***

(0.009) (0.009) (0.017) (0.017)

Inte rest rate differential i n absolute value 0.017*** 0.017*** 0.016*** 0.016*** 0.033*** 0.033*** 0.034* ** 0.034** *

(0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.005) (0.005)

Intercept 0.037*** 0.037*** 0.052*** 0.051*** 0.045*** 0.061*** 0.039*** 0.052***

(0.002) (0.002) (0.003) (0.003) (0.003) (0.004) (0.003) (0.005)

No. of observations 2235 2235 2147 2147 2314 2314 2225 2225

Note. Resultsfrom IV estimation using panel data with countryxedeffects arereported.We truncate outliers forreal exchangerate volatility, andoutliers forTI, respectively. Asterisks *,

**, and *** indicate 10%, 5%, and 1% statistical signicance, respectively.

Table 3A

Effects of TI on real exchange rate volatility: Controlling for the exchange rate regime.

Robustness checks

Controlling for the exchange rate regime

[1] [2] [3] [4]

Real exchange rate volatility at timet 1 0.138*** 0.137***

(0.025) (0.025)

TI (maximum) 0.031*** 0.029***

(0.008) (0.008)TI (average) 0.049*** 0.045***

(0.012) (0.012)

Interest rate differential in absolute value 0.035*** 0.035*** 0.035*** 0.035***

(0.005) (0.005) (0.005) (0.005)

Fixed exchange rate regime dummy 0.017*** 0.018*** 0.015*** 0.017***

(0.005) (0.005) (0.005) (0.005)

Intercept 0.035*** 0.035*** 0.029*** 0.029***

(0.005) (0.005) (0.005) (0.005)

No. of observations 1653 1653 1575 1575

Note. Results from IV estimation using panel data with country xed effects are reported. We drop all pairs involving currencies linked to trade-weighted exchange rate indices. These

include AUD and NZD over 198083, SEK and NOK over 198092, and SGD over 19802005. We also include axeddummy variable which takes on a value of one for currency

pairs, KRW/USD over 198096, MXN/USD over 198093, TRY/USD over 198099, and CHF/EUR over 198081 under the xed exchange rate regimes, and a value of zero, otherwise. As-

terisks *, **, and *** indicate 10%, 5%, and 1% statistical signicance, respectively.

13 These measures are admittedly very imperfect, as they fail to capture statements

about future policy, asset purchases (such as quantitative easing), and other tools used

by policymakers inuence currency markets. SeeEdison (1993)andSarno and Taylor

(2001)for in depth discussions about proxies for intervention operations.

14 When we use percents instead of rank orders, there is little difference between high

andlow TIcurrency pairs.The useof percentsdoesnot changeour main resultson govern-

ment intervention.




7/16

the direct effect of interest differentials (minus bidask spreads) being

credited/debited daily to traders' accounts. But there is also an indirect

effect. As is well-known, contrary to what uncovered interest parity (UIP)

would predict, in the data high-interest currencies tend to appreciate. A

vast literature documents the positive average returns of the carry trade,

a strategy that prots fromthisanomaly by borrowing low-interest curren-

cies to invest in high-interest ones.15 We thus adopt the carry trade as a

benchmark, and ask whether our ndings on mean reversion can help us

improve on this well-known strategy. Our exercise resembles that of

Jord and Taylor (2012), who also include PPP as a predictor in a sophisti-

cated version of the carry trade.16 The novelty in our paper is that we also

explore whether gains from conditioning on PPP depend on TI.

For the currencies in our sample over the period January 1986

December 2012, we compare a plain carry trade strategy with an

Table 3D

Effects of TI on real exchange rate volatility: Subsampling major vs. minor currency pairs.

Robustness checks

42 major currency pairs 49 minor/exotic currency pairs

[1] [2] [3] [4] [1] [2] [3] [4]Real exchange rate volatility at timet 1 0.104*** 0.104*** 0.090*** 0.091***

(0.032) (0.032) (0.029) (0.029)

TI (maximum) 0.035*** 0.031*** 0.039*** 0.039***

(0.006) (0.007) (0.014) (0.014)

TI (average) 0.053*** 0.047*** 0.063*** 0.062***

(0.010) (0.010) (0.022) (0.023)

Intere st rate differe ntial in absolute value 0.201*** 0.199*** 0.184*** 0.182*** 0.030*** 0.030*** 0.032*** 0.031***

(0.021) (0.021) (0.022) (0.022) (0.005) (0.005) (0.005) (0.005)

Intercept 0.040*** 0.041*** 0.035*** 0.037*** 0.051*** 0.051*** 0.061*** 0.061***

(0.003) (0.003) (0.003) (0.004) (0.007) (0.007) (0.009) (0.009)


Note. ResultsfromIV estimation using panel data with countryxedeffects arereported.91 currencypairs aredivided into42 major and49 minor/exoticcurrencypairs. Asterisks *, **,and

*** indicate 10%, 5%, and 1% statistical signicance, respectively.

Table 3E

Effects of TI on real exchange rate volatility: Dening volatility using different time windows.

Robustness checks

3-year window 6-year window

[1] [2] [3] [4] [1] [2] [3] [4]

Real exchange rate volatility at timet 1 0.038 0.040 0.062 0.062

(0.039) (0.039) (0.062) (0.062)

TI (maximum) 0.069*** 0.058*** 0.065*** 0.048**

(0.016) (0.017) (0.022) (0.024)

TI (average) 0.105*** 0.088*** 0.098*** 0.073***

(0.024) (0.026) (0.033) (0.036)

Intere st rate differe ntial in absolute value 0.064*** 0.063** * 0.075*** 0.074*** 0.110*** 0.109* ** 0.115*** 0.114***

(0.010) (0.010) (0.011) (0.011) (0.016) (0.016) (0.016) (0.016)

Intercept 0.070*** 0.070*** 0.054*** 0.055*** 0.096*** 0.095*** 0.051*** 0.051***

(0.007) (0.007) (0.007) (0.008) (0.009) (0.009) (0.010) (0.010)


Note. Resultsfrom IV estimation using panel data with countryxedeffects arereported.Volatility is computed over3-year and6-yearperiods.Asterisks *, **,and ***indicate 10%,5%, and1% statistical signicance, respectively.

Table 3C

Effects of TI on real exchange rate volatility: Subsamplingrst versus second half of sample period.

Robustness checks

Subperiod for 19801992 Subperiod for 19932005

[1] [2] [3] [4] [1] [2] [3] [4]

Real exchange rate volatility at timet 1 0.108*** 0.110*** 0.103*** 0.103***

(0.032) (0.032) (0.030) (0.030)

TI (maximum) 0.041*** 0.038*** 0.032*** 0.028***

(0.012) (0.012) (0.009) (0.010)TI (average) 0.063*** 0.059*** 0.048*** 0.043***

(0.018) (0.019) (0.014) (0.015)

Interest rate differential in absolute value 0.017** 0.016** 0.012 0.011 0.044*** 0.044*** 0.044*** 0.044***

(0.007) (0.007) (0.008) (0.008) (0.006) (0.006) (0.006) (0.006)

Intercept 0.039*** 0.040*** 0.053*** 0.053*** 0.042*** 0.042*** 0.037*** 0.037***

(0.005) (0.005) (0.005) (0.005) (0.004) (0.004) (0.005) (0.005)


Note. Resultsfrom IV estimationusing panel data with countryxedeffects arereported.The entire sampleperiodis dividedinto twosubperiods: 19801992 (arsthalf)and 19932005

(a second half). Asterisks *, **, and *** indicate 10%, 5%, and 1% statistical signicance, respectively.

15 The protability of carry trades has been documented byBrunnermeier et al. (2008)

andBurnside et al. (2006)amongmany others. While the failureof UIP has long been re-

ferredto as theforward premiumpuzzle, recentworkby Lustiget al.(2011) and Menkhoff

et al.(2012)hasgonea long way towards reconciling theprotabilityof carry trades with

standard asset pricing theory by identifying risk factors that explain excess returns.

16 In addition toJord and Taylor (2012), there have been other approaches seeking to

improve the performance of carry trade, mostly by reducing risk. For instance, some au-

thors have proposed diversication (Burnside et al., 2006), the use of options (Burnside

et al., 2011).




8/16

augmented one. The plain strategy enters a trade (long currency A,

short currency B) if the interest rate differential itA it

B exceeds a thresh-

old spread it, i.e., if

iAti

Btit: 7

We experiment with four specications of the thresholdit. In therstthree, it is constant at 1,2, or 3%. Inthe fourth, we consideran inter-

est differential to be high only if it is higher than others available at the

time. Thus, we setitequal toitmed

itmin, the difference between the

median and minimum interest rates in our sample. For a currency

A

Fig. 2.(A) GIs for 35 highest TI currency pairs. (B) GIs for 35 lowest TI currency pairs.




9/16

pair, if the difference between the higher and the lower interest rates is

less than it, the strategy is inactive and no trade is entered.

The augmented carry strategy buys currency A against B if, in

addition to the interest condition (7) being satised, currency A

is undervalued vis--vis currency B in the following sense. The 12-

month lagged real exchange rateQAB,t12 (i.e., the price of A's goods

relative to B's goods) times a factor must be below the long-run

averageQAB;t. That is,

QAB;t12

QAB;t

:

8

B

Fig. 2(continued).




10/16

The use of a lagged real exchange rate captures the idea behind

the J-curve, i.e., that it takes some time for exchange rate misalignments

toinuence trade.17 As a measureof the long-run average, we compute

real exchange rate's 15-year moving average.18

QAB;t

X180s1

QAB;ts

180

The factor captures the degree to which currency A must be

undervalued to enter a trade. If= 0, the PPP condition(8)always

holds, and the augmented carry strategy is just the plain carry. As

increases, Eq.(8)becomes more stringent, allowing fewer trades. If

b1, Eq.(8) allows currency A to be bought as long as it is not tooovervalued. For instance, if= 2/3, currency A can be bought against

B even if it is a bit expensive; specically, as long as it is less than 50%

overvalued.If= 1, condition(8) holds only if A is undervaluedrelative

to B. Finally, if N1, A can only be bought if undervalued by a given

margin. For example, if= 3/2,Eq. (8) holdsonly if A is so undervalued

that the (lagged) real exchange rate is below 2/3 of its long-term aver-

age. As continues to increase, the PPP becomes more stringent, and in

the limit it is never satised, meaning that the augmented PPP strategy

is always idle.19

The augmented carry ( N 0) is more selectivethan theplain carry

(= 0), since it requires more conditions and enters fewer trades. The

key trade-off when choosing is as follows. A higher tends to raise the

average pro

tability of the trades entered, but it also means that, byentering fewer trades, investors forego opportunities to prot from

interest differentials and diversify their portfolio. To nd the optimal

levels of, we evaluate the performance of the plain and augmented

strategies separately for the set of 35 high and 35 low TI currency

pairs fromTable 4. To compute the returns of the plain carry, for every

currency pair, we check whether the interest rate condition (7)is

satised. If yes, the pair is active. If not, it is inactive. The return of an

active pair is given by

Rt1SAB;t1

SAB;t 1 i

At1i

Bt1tc

12

" #; 9

whereSAB,tis the nominal exchange rate measured as the price of one

unit of currency A in terms of currency B, and tcis a transaction cost,set at 1% per annum.20 Thereturn of an inactivepair is zero. Theportfolio

return Rt+ 1PF (for high andlow TI), is theequally weighted average of the

returns of active pairs. If no pairs are active, the portfolio return Rt+ 1PF is

zero. To simulate the augmented carry we follow the same steps, with

the only difference being thatas explained abovea pair must satisfy

both the interest rate condition(7) and the PPP condition(8) to be

active.

For each strategy, we compute 27 years of monthly returns from

January 1986 to December 2012. To evaluate performance, we focus

on the annualized Sharpe ratio dened as

SharpeMean RPF

SD RPF

ffiffiffiffiffiffi

12p

; 10

where multiplying byffiffiffiffiffiffi

12p

converts a monthly ratio into an annual one.

The evolution of Sharpe ratios as a function ofis plotted in Fig. 4 for

all specications ofit. The case with= 0 corresponds to the plain

carry. Forb 0.5, PPP deviations in the sample are too small to violate

the PPP condition, and the augmented carry remains the same as the

plain one. Starting at around= 0.5 for low TI and 0.6 for high TI, we

start nding cases where the high-interest currency is overvalued

enough to violate the PPP condition. The PPP condition deactivates

these trades, which tends to raise Sharpe ratios, especially in the low

TI group. Sharpe ratios increase forbetween approximately 0.6 and

0.95 in the high TI group and 0.5 and 1 in the low TI group. Beyond

0.95, or 1, increases in tend to lower Sharpe ratios, as the opportunity

cost from foregoing a growing number of trades outweighs the gains

from increased average quality of trades. This decline is more pro-nounced in the high TI group. In sum, gains from augmenting the

carry strategy are typically greater in the low TI portfolio, because

there is a wider range of values offor which the augmented carry out-

performs the plain carry, and because there is typically a higher

Table 4

Half-life estimates for real exchange rates.

High TI currency pairs Low TI currency pairs

Half-life Half-life

USD/CAD 32 TRY/SEK 23

USD/MXN 16 CAD/AUD 11

USD/JPY 31 TRY/KRW 43

CHF/EUR 5 SEK/AUD 12

GBP/EUR 26 CHF/SGD 29

TRY/EUR 24 MXN/CAD 28

USD/KRW 7 NZD/CAD 35

KRW/JPY 13 CHF/AUD 36

NZD/AUD 35 CHF/KRW 17

USD/SGD 56 CHF/NOK 23

SEK/NOK 36 SEK/CAD 21

SEK/EUR 15 NOK/KRW 7

JPY/AUD 22 SEK/KRW 12

GBP/NOK 3 GBP/MXN 17

USD/GBP 14 CHF/CAD 41

SGD/JPY 25 MXN/KRW 22

USD/EUR 15 SEK/SGD 19

NOK/EUR 6 TRY/CAD 33

GBP/SEK 12 SGD/NOK 28

USD/AUD 17 SGD/CAD 53

USD/TRY 39 CHF/MXN 21

NZD/JPY 24 TRY/AUD 39

USD/NZD 19 TRY/NOK 41USD/CHF 18 TRY/SGD 32

JPY/EUR 27 SEK/NZD 23

USD/SEK 18 SEK/MXN 49

GBP/CHF 27 CHF/NZD 6

GBP/TRY 17 NZD/MXN 24

GBP/JPY 31 SGD/MXN 26

SGD/AUD 16 NOK/AUD 16

SGD/KRW 1 MXN/AUD 27

KRW/AUD 4 TRY/NZD 27

GBP/AUD 21 NOK/NZD 6

GBP/NZD 12 TRY/MXN 27

USD/NOK 23 NOK/MXN 48

Average 20.20 26.34

Note. The half-life is measured as the discrete number of months taken until the shock to

the level of the real exchange rate has fallen below half.

17 We have chosen a 12 month lag after experimenting with multiple specications.

While the best lags seem to range between 9 and 15 months, results are still qualitatively

similar for lags between 6 and 24 months, and worsen substantially outside this range.18 Weuse dataon real exchangerates from January 1971to December 1985to compute

the initial average real exchange rate. Experimenting with the number of lagsin the mov-

ing average, we nd that, as the n umber of lags rises, the moving average becomes more

stable and useful as a predictor. These gains, however, peter out as the number of lags

grows. On the other hand, more lags mean losing more observations at the start of the

sample period, because they are needed to compute the rst moving average. Our choice

of 15 years balances these two effects. As long as the moving average contains at least

10 years, results remain fairly similar.

19 It is important to notethat,although it involvesa moving average,the augmented PPP

carry is not a momentum strategy. Momentum strategies buy currencies when the ex-

change rate is greaterthanits movingaverage. Thesimplestexample is BuyifStN MA(1),

which is equivalent toBuy ifStN St 1. Our PPP conditionespecially for high values of

does the opposite, buying currencies that have substantially depreciated, i.e., buying

when the exchange rate is below the moving average.20 In spot foreign exchange markets, transaction costs include a bidask spread applied

at the level of the exchange rate, and another bidask spread applied to the interestrates.

These spreadsare different acrosstime periods, currency pairs, andbrokers. We havecho-

sen 1% per annum as a rough average based on spreads charged by forex brokers such as

OANDA, FXCM, and others.




11/16

maximum gain in Sharpe ratio relative to the plain carry. The optimal

level ofis also higher in the low TI group. Specically, Sharpe ratiospeak for= 0.95, 0.95, 0.97, and 0.95 in the high TI group and 1, 1, 1,

and 1.14 in the low TI group, for itrespectively equal to 1%, 2%, 3%,

and itmed

itmin. These optimal values of, along with peak Sharperatios,

are reported inTable 6, panel (A). For both high and low TI, in all four

specications ofit, the Sharpe ratio for the augmented carry is higher

than for the plain carry. Gains from conditioning on PPP are also

displayed inFig. 5, where we plot the evolution of 1 dollar over time

under both strategies. In the high TI case, the augmented carry earns

higher average returns than the plain carry. Moreover, the augmentedstrategy is less risky, largely avoiding the 2008 crash suffered by the

plain carry. In the low TI case, the augmented carry's mean return sur-

passes the plain carry's by an even wider margin than in the high TI

case, while volatility is similar for both strategies.21

Thisin-sample comparison, however, may exaggeratethe benetsof

conditioning on PPP, because is chosen with thebenet of hindsight. A

fairertest is to compare both strategies out-of-sample. To simulate the

out-of-sample augmented carry, we consider a hypothetical investor

whofor each yeart{1994,,2012}choosesat the start of the

year using only the data available up to that point. That is, the investor

setsat the level that maximizes the augmented carry's Sharpe ratio

over the period January 1986December t 1, and updatesyearly.

For both high and low TI, and for all four specications of the interest

rate condition, the out-of-sample values of

uctuate within a relative-ly narrow range of the in-sample values reported above, with the max-

imizing value ofbeing higher in the low TI group most years. Using

these values of, we simulate the augmented carry over theperiod Jan-

uary 1994December 2012, and report performance statistics in Table 6

(B). As expected, the gains from conditioning on PPP weaken to some

extent, especially in the high TI case. Forit3%, anditimedt imint ,out-of-sample results are similar to in-sample results. The augmented

t


12/16

carry is clearly superior to the plain carry, both due to higher returns

and lower risk, most notably at the time of the 2008 crash. However,

forit1%and it2%, the augmented carry has similar volatilityand slightly lower returns than the plain carry, resulting in a mildly

lower Sharpe ratios. Inspecting all cases together in Fig. 6(A), the

augmented carry comes out slightly behind in the rst two graphs,

but clearly ahead in the third and fourth. In the low TI case, results re-

main favorable to the augmented carry. As reported inTable 6(B), the

augmented carry has higher Sharpe ratios than the plain carry for

three out of four specications of the interest rate condition, and higher

mean returnsfor all four specications. This is clearly visible in Fig. 6(B),

where the augmented carrynishes ahead of the plain carry in all four

plots.Overall, we nd conditioning on PPP to be more useful in the low TI

portfolio, where exchange rates tend to deviate further from long-run

values. This raises potential losses from wrong predictions and gains

from correct ones, as compared with the high TI case. Since interest

differentials are similar in both groups, staying out of trades has a

similar opportunity cost, while predicting larger swings in the low TI

case provides a greater benet.

6. Conclusion

This paper explores the interaction between exchange rate volatility

and fundamentals by examining the role of TI in the reversion of ex-

change rates to long-run equilibrium values, as given by purchasing

power parity (PPP). Following the recent literature on nonlinearity,we estimate an ESTAR model, which allows the speed at which

exchange rates converge to their long-run equilibrium to depend on

the size of the deviations. We nd estimates of the half-lives of devia-

tions from PPP to be higher the less intense the trade relationship

between two countries. These results continue to hold as we perform

a series of robustness tests, such as including/excluding interest rates

as explanatory variables, focusing on different subsamples, and

experimenting with different window widths to compute volatility.

When including interest rates, we nd that exchange rate volatility

increases with the absolute value of interest rate differentials, which is

consistent with the notion that carry trades tend to exacerbate uctua-

tions in currency markets. We also verify that the faster convergence to

equilibrium values observed for high TI pairs does not appear to be

driven by Central Bank intervention. Finally, we investigate whether

our ndings can be useful to improve the performance of a well-

known currency trading strategy, the carry trade. We consider strate-

gies that combine a carry-trade componentinvesting in high-interest

rate currencieswith a fundamental componentpurchasing curren-

cies only if undervalued according to relative PPP. Our ndings suggest

that an augmented carry trade strategy that conditions on PPP funda-

mentals tends to perform betterin terms of higher Sharpe ratios

than a plain carry strategy which blindly chases interest rate differen-

tials. These ndings hold in- and out-of-sample, although they are a

bit weaker in the latter case. Gains from conditioning on PPP are

generally greater for low TI currency pairs.

Acknowledgments

This paper has beneted from discussion with or comments by

Richard Baillie, Kirt Butler, Jinill Kim, Seunghwa Rho as well as by the

Editor, Eric van Wincoop, and two anonymous referees. We would also

like to thank participants at Yonsei University, Korea University, the

2010 Midwest Macroeconomics Meetings, 2010 Midwest Econometrics

Group Annual Meetings, and 2011 Eastern Finance Association Annual

Meetings, 2012 Econometric Society's North American Summer Meet-

ings, and 2012 Australasian Meeting of Econometric Society for helpful

comments. Any remaining errors are solely the authors' responsibility.

Appendix A

In this appendix,we briey introducethe ESTAR model,and describe

how to estimate half-lives of deviations from PPP.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Threshold ()

High TI

Low TI

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-0.4

-0.2

00.2

0.4

0.6

0.8

1

1.2

1.4

Threshold ()

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Threshold ()

0 0.2 0 .4 0 .6 0.8 1 1.2 1.4 1.6 1 .8 2

-0.4

-0.2

0

0.20.4

0.6

0.8

1

1.2

1.4

Threshold ()

AunnualizedSharperatio

Aunnualize

dSharperatio

AunnualizedSharperatio

Aunnu

alizedSharperatio

(A)

(B)

(C)

(D)

Fig. 4.Annualized Sharpe ratios as a function of the PPP threshold ().




13/16

A.1. The ESTAR model

The regime-switching model known as Smooth Transition Auto-

regressive (STAR), was developed byGranger and Tersvirta (1993)

and Tersvirta (1994). In this model, adjustment takes place every

period but the speed of adjustment varies with the extent of the

deviation from equilibrium. When reparameterized in rst difference

form, the STAR model for the real exchange rateqtcan be written as

qtqt1

Xp1

j

1

jqtj qt1Xp1

j

1

j qtj

24

35 q td; ; c t

11

where qt j = qt j qt j 1, {qt} is a stationary and ergodic process,

t iid(0, 2), and () is the transition function that determines

the degree of mean reversion and itself governed by the parameter

, which determines the speed of mean reversion to PPP. The delay

parameter d (N0) is an integer. The ESTAR model is the variant

of the STAR model where transition is governed by the exponential

function

qtd; ; c 1exp qtdc 2=qtd with N0h

12

whereqtdis a transition variable, qtd is the standard deviation of

qt d, is a slope parameter, and c is a location parameter. The

restriction on the parameter (N 0) is an identifying restriction. Theex-

ponential functionin Eq. (12) is bounded between 0 and 1,and depends

on the transition variableqtd. The values taken by the transition var-

iableqtd and the transition parameter together will determine the

speed of mean reversion to PPP.22 ESTAR models are estimated by non-

linear least squares (NLS), with the starting values obtained from a grid

search over andc. The estimations are also implemented with the se-

lected lag orderp and delay parameterd which are suggested by the

partial autocorrelation function (PACF) and the linearity tests results,

respectively, for both high and low TI currency pairs.

A.2. Estimation of half-lives of deviations from PPP

We investigate the dynamic adjustment in response to the shock of

the estimated ESTAR model by computing generalized impulse

response functions. The generalized impulse response function (GI),

proposed by Koop et al. (1996) avoidsthe problem of using future infor-

mation by taking expectations conditioning only on the history and on

the shock. GI may be considered as the realization of a random variable

dened as

GIq h; t; t1 E qthjt; t1

E qthjt1 13

Table 6

Summary statistics for carry trade portfolios.

(A) In-sample: Jan. 1986Dec. 2012

High TI currency pairs

it1% it2% it3% itimedt imintPlain Augmented Plain Augmented Plain Augmented Plain Augmented

= 0 = 0.95 = 0 = 0.95 = 0 = 0.97 = 0 = 0.95

Average 1 month return 0.377% 0.450% 0.465% 0.562% 0.518% 0.622% 0.633% 0.724%Standard deviation 0.016 0.017 0.019 0.018 0.021 0.020 0.024 0.021

Annualized Sharpe ratio 0.811 0.930 0.860 1.058 0.858 1.086 0.918 1.197

Low TI currency pairs


= 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1.14

Average 1 month return 0.432% 0.618% 0.495% 0.664% 0.550% 0.747% 0.626% 0.775%

Standard deviation 0.017 0.018 0.019 0.020 0.021 0.022 0.024 0.027


(B) Out-of-sample: Jan. 1994Dec. 2012

High TI currency pairs

it1% it2% it3% itimed

t imin

t

Plain Augmented Plain Augmented Plain Augmented Plain Augmented

= 0 Varying = 0 Varying = 0 Varying = 0 Varying




Low TI currency pairs


= 0 Varying = 0 Varying = 0 Varying = 0 Varying




22 For any given value ofqt d, the transition parameterdetermines the slope of the

transitionfunction,and thus thespeedof transitionbetween tworegimes,with lowvalues

of implying slower transitions.




14/16

for h = 0,1,2.InEq. (13), theexpectation ofqt+h given thatthe shock

occurs at time tis conditional only on the history and on the shock. We

generate GI functions using the Monte Carlo integration method

developed by Gallant et al. (1993). For the history and the initial

shock, we computeGIq(h,,t1) for horizonsh=0,1,2,100. The

conditional expectations in Eq.(13)are estimated as the means over

(A)HIGH TI CURRENCY PAIRS (B)LOW TI CURRENCY PAIRS

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

Plain CarryAugmented Carry

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

Fig. 5.In-sample performance of carry trade portfolios (Jan. 1986Dec. 2012): evolution of one dollar over time.




15/16

2000 realizations ofqt+ h, accomplished by iterating on the ESTAR

model, with and without using the selected initial shock to obtainqt

and using randomly sampled residuals of the estimated ESTAR model

elsewhere. Impulse responses for the level of the real exchange rate, qtare obtained by accumulating the impulse responses for the rst differ-

ences. The initial shock is normalized to 1, and the half-lives of real

(A)HIGH TI CURRENCY PAIRS (B)LOW TI CURRENCY PAIRS

94 96 98 00 02 04 06 08 10 12

1

2

3

4

Plain Carry

Augmented Carry

94 96 98 00 02 04 06 08 10 12

1

2

3

4

94 96 98 00 02 04 06 08 10 12

1

2

3

4

94 96 98 00 02 04 06 08 10 12

1

2

3

4

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

Fig. 6.Out-of-sample performance of carry trade portfolios (Jan. 1994Dec. 2012): evolution of one dollar over time.




16/16

exchange rates to the shock are calculated by measuring the discrete

number of months taken until the shock to the level of the real

exchange rate has fallen below half.

References

Bec, F., Ben Salem, M., Carrasco, M., 2010. Detecting Mean Reversion in RealExchange Rates from a Multiple Regime STAR Model. Ann. Econ. Stat. 99 (100),395427.

Betts, C.M., Kehoe, T.J., 2008.Real exchange rate movements and the relative price of

non-traded goods. Research Department Staff Report 415, Federal Reserve Bankof Minneapolis.

Bhansali, V., 2007.Volatility and the carry trade. J. Fixed Income 17, 7284.Broda, C., Romalis, J., 2009.Identifying the relationship between trade and exchange rate

volatility. Commodity Prices and Markets, East Asia Seminar on Economics, 20.Brunnermeier, M.K., Nagel, S., Pedersen, L.H., 2008. Carry trades and currency crashes.

NBER Macroecon. Annu. 23, 313347.Burnside, C., Eichenbaum, M., Kleshchelski, I., Rebelo, S., 2006.The returns to currency

speculation. NBER Working Paper 12489.Burnside, C., Eichenbaum, M., Kleshchelski, I., Rebelo, S., 2011.Do peso problems explain

the returns to the carry trade? Rev. Financ. Stud. 24, 853891.Calvo, G.A., Reinhart, C.M., 2002.Fear ofoating. Q. J. Econ. 107, 379408.Edison, H.J., 1993.The effectiveness of central-bank intervention: a survey of the litera-

ture after 1982. Special Papers in International Economics No. 18Department ofEconomics, Princeton University.

Gallant, A.R., Rossi, P.E., Tauchen, G., 1993.Nonlinear dynamic structures. Econometrica61, 871908.

Granger, C.W.J., Tersvirta, T., 1993. Modelling Nonlinear Economic Relationships. Oxford

University Press, New York.Jord, O., Taylor, A.M., 2012.The carry trade and fundamentals: nothing to fear but FEERitself. J. Int. Econ. 88, 7490.

Kapetanios, G., Shin, Y.,Snell, A.,2003. Testing fora unit root inthe nonlinear STARframe-work. J. Econ. 112, 359379.

Koop, G., Pesaran, M.H., Potter, S., 1996.Impulse response analysis in nonlinear multivar-iate models. J. Econ. 74, 119147.

Lustig, H., Roussanov, N., Verdelhan, A., 2011.Common risk factors in currency markets.Rev. Financ. Stud. 24, 37313777.

Mark, N.C., 1995.Exchange rates and fundamentals: evidence on long-horizon predict-ability. Am. Econ. Rev. 85, 201218.

Meese, R.A., Rogoff, K., 1983.Empirical exchange rate models of the seventies: do they tout of sample? J. Int. Econ. 14, 324.

Menkhoff, L., Sarno, L., Schmeling, M., Schrimpf, A., 2012.Carry trades and global foreign

exchange volatility. J. Finance 67, 681718.Michael, P., Nobay, A.R., Peel, D.A., 1997.Transactions costs and nonlinear adjustment inreal exchange rates: an empirical investigation. J. Polit. Econ. 105, 862879.

Molodtsova, T., Papell, D.H., 2009. Out-of-sample exchange rate predictability with Taylorrule fundamentals. J. Int. Econ. 77, 137276.

Norman, S., 2009. Testing for a unit root against ESTAR nonlinearity with a delayparameter greater than one. Econ. Bull. 29, 21522173.

Reinhart, C.M., Rogoff, K.S., 2009.This Time is Different: Eight Centuries of Financial Folly.Princeton University Press, Princeton, NJ.

Rogoff,K., 2008. Interview with The Region.FederalReserve Bankof Minneapolis. Decem-ber Issue, 18-29.

Saikkonen, P., Luukkonen, R., 1988.Lagrange multiplier tests for testing non-linearities intime series models. Scand. J. Stat. 15, 5568.

Sarno, L., Taylor, M.P., 2001.Ofcial intervention in the foreign exchange market: is iteffective and, if so, how does it work? J. Econ. Lit. 39, 839868.

Taylor, M.P., Peel, D.A., Sarno, L., 2001.Nonlinear mean-reversion in real exchange rates:toward a solutionto the purchasing power parity puzzles.Int. Econ. Rev.42, 10151042.

Tersvirta, T., 1994. Specication, estimation and evaluation of smooth transitionautoregressive models. J. Am. Stat. Assoc. 89, 208218.

http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0005http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0005http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0005http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0005http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0005http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0165http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0165http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0165http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0010http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0010http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0010http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0170http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0170http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0020http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0020http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0020http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0020http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0175http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0175http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0025http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0025http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0025http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0025http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0030http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0030http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0030http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0030http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0030http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0180http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0180http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0180http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0050http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0050http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0050http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0050http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0055http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0055http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0075http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0075http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0075http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0075http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0080http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0080http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0080http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0080http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0085http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0085http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0085http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0085http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0090http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0090http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0090http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0090http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0100http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0100http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0100http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0100http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0110http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0115http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0115http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0115http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0115http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0120http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0120http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0120http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0120http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0125http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0125http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0125http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0125http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0130http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0130http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0130http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0130http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0135http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0135http://refhub.elsevier.com/S0022-1996(14)00010-5/rf8000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf8000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf9000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf9000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf9000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf9000http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0145http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0145http://refhub.elsevier.com/S0022-1996(14)00010-5/rf0145http://refhub.elsevier.com/S0022-1996(14)00010-5/r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